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Question: Answered & Verified by Expert
If the amplitude of $z-2-3 i$ is $\frac{\pi}{4}$, then the locus of $z=x+i y$ is :
MathematicsComplex NumberAP EAMCETAP EAMCET 2003
Options:
  • A $x+y-1=0$
  • B $x-y-1=0$
  • C $x+y+1=0$
  • D $x-y+1=0$
Solution:
2763 Upvotes Verified Answer
The correct answer is: $x-y+1=0$
We have, $z-2-3 i=x+i y-2-3 i$
$=(x-2)+i(y-3)$
Given, $\tan ^{-1}\left(\frac{y-3}{x-2}\right)=\frac{\pi}{4} \Rightarrow y-3=x-2$
$\therefore \quad x-y+1=0$

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